If #sqrty=64x^3#, then what is #root(3)y#?

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Answer 1 · 2017-02-09T10:22:45

#16x^2#

If we have

#sqrty=64x^3#

then what is the value of #root(3)y#?

We can do this by squaring then taking the cube root of y, in effect taking both sides to the power of #2/3#:

#(sqrty)^(2/3)=(64x^3)^(2/3)#

We can use the rule that #(x^a)^b=x^(ab)#

#root(3)y=(2^6x^3)^(2/3)=2^(6xx(2/3))x^(3xx(2/3))=2^4x^2=16x^2#